Can someone help me in this trig question, please? thanks A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates 5pi/12

Answers

Answer 1

Answer:

The exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).

The position

Since the position of the carousel is (x, y) = (20cosθ, 20sinθ) and we need to find the position when θ = 5π/12 = 5π/12 × 180 = 75°

So, substituting the value of θ into the positions, we have

(20cos75°, 20sin75°)

The value of 20cos75°

20cos75° = 20cos(45 + 30)

Using the compound angle formula

cos(A + B) = cosAcosB - sinAsinB

With A = 45 and B = 30

cos(45 + 30) = cos45cos30 - sin45sin30

= 1/√2 × √3/2 - 1/√2 × 1/2

= 1/2√2(√3 - 1)

= 1/2√2(√3 - 1) × √2/√2

= √2(√3 - 1)/4

= (√6 - √2)/4

= (-√2 + √6)/4

So, 20cos75° = 20 × (-√2 + √6)/4

= 5 (-√2 + √6)

The value of 20sin75°

20sin75° = sin(45 + 30)

Using the compound angle formula

sin(A + B) = sinAcosB + cosAsinB

With A = 45 and B = 30

sin(45 + 30) = sin45cos30 + cos45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= 1/2√2(√3 + 1)

= 1/2√2(√3 + 1) × √2/√2

= √2(√3 + 1)/4

= (√6 + √2)/4

= (√2 + √6)/4

So, 20sin75° = 20 × (√2 + √6)/4

= 5(√2 + √6)

Thus, (20cos75°, 20sin75°) = 5 (-√2 + √6), 5(√2 + √6).

So, the exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).

Learn more about position here:

brainly.com/question/11001232

Answer 2

Answer: $\bf \textit{the position of the rider is clearly }20cos\left( (5\pi )/(12) \right)~~,~~20sin\left( (5\pi )/(12) \right)\n\n-------------------------------\n\n\cfrac{5}{12}\implies \cfrac{2+3}{12}\implies \cfrac{2}{12}+\cfrac{3}{12}\implies \cfrac{1}{6}+\cfrac{1}{4}\n\n\n\textit{therefore then }\qquad \cfrac{5\pi }{12}\implies \cfrac{1\pi }{6}+\cfrac{1\pi }{4}\implies \cfrac{\pi }{6}+\cfrac{\pi }{4}\n\n-------------------------------$

$\bf \textit{Sum and Difference Identities}\n\nsin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta)\n\ncos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)\n\n-------------------------------\n\ncos\left( (\pi )/(6)+(\pi )/(4) \right)=cos\left( (\pi )/(6)\right)cos\left((\pi )/(4) \right)-sin\left( (\pi )/(6)\right)sin\left((\pi )/(4) \right)$

$\bf cos\left( (\pi )/(6)+(\pi )/(4) \right)=\cfrac{√(3)}{2}\cdot \cfrac{√(2)}{2}-\cfrac{1}{2}\cdot \cfrac{√(2)}{2}\implies \cfrac{√(6)}{4}-\cfrac{√(2)}{4}\implies \boxed{\cfrac{√(6)-√(2)}{4}}\n\n\nsin\left( (\pi )/(6)+(\pi )/(4) \right)=sin\left( (\pi )/(6)\right)cos\left( (\pi )/(4) \right)+cos\left( (\pi )/(6)\right)sin\left((\pi )/(4) \right)$

$\bf sin\left( (\pi )/(6)+(\pi )/(4) \right)=\cfrac{1}{2}\cdot \cfrac{√(2)}{2}+\cfrac{√(3)}{2}\cdot \cfrac{√(2)}{2}\implies \cfrac{√(2)}{4}+\cfrac{√(6)}{4}\implies \boxed{\cfrac{√(2)+√(6)}{4}}\n\n-------------------------------\n\n20\left( \cfrac{√(6)-√(2)}{4} \right)\implies 5(-√(2)+√(6))\n\n\n20\left( \cfrac{√(2)+√(6)}{4} \right)\implies 5(√(2)+√(6))$

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How to find the value of this expression

Answers

32 because 64 divided by 2 equals 32

The square root is 64 is 8. Then times that by 2 your answer is 16. Hope that helps.

Which permanent teeth eruption usually occurs first? A. Central incisors. B. Lateral incisors. C. Cuspids (canines). D. First premolars (Bicuspids).

Answers

Answer: Letter A

Step-by-step explanation: because it is located at the front of the jaw and is the closest to the dental lamina, the source of tooth development in the jawbone

1- Find the surface area and volume of each solid figure.2-Show the equations you used.

PLEASE HELP!!!!!!! 20 points

Answers

Answer:

Volume

Figure 1 = 56 cube units

figure 2 = 60 cube units

figure 3 =72 cube units

Surface area

Figure 1 = 100 square units

figure 2 = 104 square units

figure 3 =108 square units

Step-by-step explanation:

From the all figure we can see that each figure made up of unit cubes

Figure 1

Surface area

Large cuboid portion =2 x (6 x 2 ) + (6 x 4) + 2 x(4 x 2) + 16

= 24 + 24 + 16 + 16 = 80 unit square

Small cuboid portion = (4 x 2) + (2 x 2) + (4 x 2) = 8 + 4 + 8 = 20

Total surface area = 80 + 20 = 100 unit square

Volume

Small cuboid = 4 x 2 = 8

Large cuboid = 6 x 4 x 2 = 48 cube unit

Total volume = 48 + 8 = 56 cubs units

Figure 2

Surface area

Total surface area =24 + 18 + 36 + 20 + 6 = 104 unit square

Volume

Small cuboid = 6 x 2 = 12

Large cuboid = 6 x 4 x 2 = 48 unit square

Total volume = 48 + 12 = 60 cube units

Figure 3

Surface area

Total surface area = 48 + 36 + 24 = 108 square units

Volume

Total volume = 6 x 4 x 3 = 72 cube units

The sum of two numbers is 100. The sum of 8 and the larger number is equal to 5 times the smaller number. What is the smaller number?

Answers

Answer:

The smaller number is 18

Step-by-step explanation:

Let the numbers be $x$ and $y$ where x is the smaller number; $y\:>\:x$ .

The sum of the numbers is 100.

$x+y=100...(1)$

The sum of 8 and the larger number is equal to 5 times the smaller number.

$y+8=5x$

$\Rightarrow y=5x-8...(2)$

Put equation (2) into equation (1).

$x+5x-8=100$

$x+5x=100+8$

$6x=108$

$x=18$

Answer:

The smaller number is 18.

Step-by-step explanation:

We have given that

The sum of two numbers is 100. The sum of 8 and the larger number is equal to 5 times the smaller number.

Let x and y are two numbers.

Let y is the larger number.

x+y = 100 eq(1)

y+8 = 5x eq(2)

From eq(1), we have

y = 100-x

Putting above eq(3) into eq(2), we have

100-x+8 = 5x

108 = 5x+x

108 = 6x

x = 108/6

x = 18

Hence, the smaller number is 18.

For f(x) = 3x + 4, find f(2) and find x such that f(x) = 17

Answers

f(x) = 3x+ 4
⇒ f(2)= 3*2+ 4= 10
The basic idea is that you replace all x values with 2 to find f(2).

f(x) = 17
⇒ 3x+ 4= 17 (for f(x)= 3x+ 4)
⇒ 3x= 17-4
⇒ 3x= 13
⇒ x= 13/3
⇒ x= 4 1/3

f(2)= 10
f(x)=17 when x= 4 1/3

Hope this helps~

Which numbers should be multiplied to obtain 175^2 − 124^2?51 and 299

51 and 51

30501 and 30749

2601 and 2601

Answers

you have to multiply 51 and 299 you will gets 15249 wich is the same as 175^2 - 124^2

Your Answer:

A.) 51 and 299

Step-by-step explanation:

In order to find out what other numbers are multiplied to obtain x, our unknown value, we must first square 175² - 124². 175² is equal to 30625 and 124² is equal to 15376. When we subtract 30625 and 15376, we get 15249. Now that we have found out our once unknown value, we will multiply the numbers from the list of choices to see which to values lead up to the product 15249. After multiplying 51 and 299, we find that they equal 15249, our desired answer.

Hope this helps y'all :D